Function for Rolling Friction

I am writing a simple programme and need a function for friction acting on a rolling sphere and I am not sure how to go about it so can you help please.

The environment will be a sphere rolling across a horizontal surface of friction f at a velocity of.v and I wish to compute the new v after a period of time t.

I guess v will be in m/s, t will be in seconds or a fraction of and f will be the friction factor where 0 is none and 1 what arrest the sphere instantly. Thus

Newv = FunctionForFriction( v , t , f )

Then if it does not make the function much more complex it would be nice if I could vary the inclination of the surface the sphere is rolling across. Where i is the inclination of the surface in degrees, thus 45 would be up hill and -45 would be down hill.

Newv = FunctionForFriction( v , t , f , i )

Also I assume that this will be in a vacuum and therefore air resistance need not be considered.

Many thanks in advance IMK
To be a part of the solution and not part of the problem

The thing is, if the ball is "rolling" perfectly, then theoretically it would keep rolling forever. The friction doesn't actually slow down the ball once it is rolling - it just makes sure that the ball is rolling instead of sliding. In real life, the air resistance and small deformations of the ball and surface are what slows it down. For example a soccer ball rolling along a pitch will lose energy crumpling blades of grass it rolls over. That crinkling is separate from friction though.

The thing is, if the ball is "rolling" perfectly, then theoretically it would keep rolling forever. The friction doesn't actually slow down the ball once it is rolling - it just makes sure that the ball is rolling instead of sliding. In real life, the air resistance and small deformations of the ball and surface are what slows it down. For example a soccer ball rolling along a pitch will lose energy crumpling blades of grass it rolls over. That crinkling is separate from friction though.

Maze, many thanks for the correction.
Then how do I apply the above to my requirment then please.
Many thanks IMK

You could make a fake "friction force" to approximately account for all the energy loss due to air resistance, deformations, etc etc. I'm not sure if the net slowdown force goes proportional to the velocity of the ball like air resistance, or if it goes proportional to the normal force on the ball like friction, or if it obeys some other rules, or if the form of the equation depends on what type of surface you are rolling on.

This would make an interesting experiment actually - to go roll some balls along the grass with a stopwatch and distance markings and figure out how it works.

My hypothesis would be that the slowdown force goes proportional to the velocity, since from experience it seems like a rolling golf ball or soccer ball spends a disproportionate amount of time rolling really slowly right before it stops, as compared to a sliding block which seems to spend more of its time going fast and then stop abruptly.